One-Loop Threshold Effects in String Unification

Like grand unification of old, string unification predicts simple tree-level relations between the couplings of all unbroken gauge groups such as $SU(3)_C$ or SU(2)_W\). I show here how to compute one-loop corrections to these relations for any four-dimensional model based on a classical vacuum of the heterotic string. The result can be used to calculate both $\sin^2\theta_W$ and $\Lambda_{\rm QCD}$ in terms of $\alpha_{\rm QED}$ and \mpl\). The original version of this paper was written in 1987 and published in Nuclear Physics in 1988. That version had a few factor-of-two errors, which lead some people into confusion. To avoid future confusion, I've written Errata; they are submitted separately to hep-th (article #9205068). This submission is the complete revised version of the paper.